A Posteriori Error Estimates for the Weak Galerkin Finite Element Methods on Polytopal Meshes

By Hengguang Li. Communications in Computational Physics, 2019

72 citations recorded by the source corpus.

In this paper, we present a simple a posteriori error estimate for the weak Galerkin (WG) finite element method for a model second order elliptic equation. This residual type estimator can be applied to general meshes such as hybrid, polytopal and those with hanging nodes. We prove the reliability and efficiency of the estimator. Extensive numerical tests demonstrate the effectiveness and flexibility of the mesh refinement guided by this error estimator. AMS subject classifications: 65N15, 65N30, 35J50

Subfields: Computational Mechanics, Electrical and Electronic Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/4fab7156b19ebb7aacf8fcfe11f44786b9a5738e